Intermediate Introduction to Stats

Running head ECON 451 1
ECON 451 Intermediate Introduction to Stats. and Econometrics I
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ECON 451 2
ECON 451 INTERMEDIATE INTRODUCTION TO STATS. AND ECONOMETRICS I
Homework 6 covers material of point (MOM and ML) and interval inference.
1. Find the method of moment estimators for the unknown parameters in the pdf
below:
a.
Solution:
This is based on a random sample Y1, Y2,...., Yn
The first and second theoretical moments for this distribution;
Hence the solution is satisfied.
b.
Use E[Y] and E[Y2]
Solution
This is based on a random sample Y1, Y2,....., Yn
The first and second theoretical moments for the normal distribution are;
The first and second sample moments are;
Solving the equation results to
and
Therefore the method of moment’s estimate of the above is;